KT and consciousness

Consciousness research has been measuring the wrong things and calling them consciousness — this paper builds a formal framework to show exactly which thing each marker actually measures.

The core problem is a conflation that runs through the entire field. When scientists validate a consciousness marker, they calibrate it against subjects who can report their experience. This bakes in a systematic blind spot: the marker ends up tracking the machinery of report — the brain systems that make a state verbally accessible and memorable — rather than experience itself. The perturbational complexity index (PCI), which compresses EEG responses to magnetic brain stimulation, is the flagship example. High PCI means the cortico-thalamic system is actively running its internal model and generating structured output. That's a statement about the report-and-memory machinery being online, not about whether there's something it's like to be that brain. Worse, PCI runs opposite in sign to good regulation: a well-regulated system makes its outputs more compressible, while PCI rises with complexity. A seizure has high PCI and catastrophically bad regulation simultaneously — a marker that reads only complexity cannot tell waking from seizure.

The paper's organizing tool is Kolmogorov Theory (KT), which treats minds as algorithmic agents that build compressive models of their world in order to persist. The central theorem (the Algorithmic Regulator Theorem) says: any system that keeps its world's behavior compressible must contain a model of that world. From this, the authors derive a three-axis taxonomy. Axis one is experience — the phenomenal fact of running a compressive model. Axis two is reportability — the downstream machinery that makes a state available for verbal output and memory. Axis three is regulation and world-modeling — how well the system controls and predicts its environment, measured by mutual algorithmic information (MAI) between system and world. The flagship markers cluster on axes two and three. None directly touches axis one.

The key asymmetry this forces: report implies (probably) experience, but absence of report does not imply absence of experience. This isn't just philosophical hedging — it has direct clinical stakes. Roughly a quarter of behaviorally unresponsive patients show covert command-following on neuroimaging. Their report machinery is severed; their modeling may be intact. The paper also reframes the oddball ERP paradigm (where brains respond to violated regularities) as a graded probe of world-model depth: the mismatch negativity reflects low-complexity local tracking and survives sleep; the P300b requires access machinery and fails without it. Crucially, MAI is operationally reachable even though Kolmogorov complexity itself is uncomputable — you establish it by prediction, not by computing any complexity number. If a brain readout lets you predict abstract rule structure in the stimulus stream, that's a witnessed lower bound on MAI at that abstraction level.

The paper proposes a "regulatory-order ladder" as a substrate-agnostic replacement for the vague phrase "level of consciousness": order zero is homeostasis, climbing through local pattern tracking, global rule detection, offline simulation, up to modeling one's own modeling. Each rung is backed by a theorem — sustaining compression at that abstraction level requires model content at that level. For experience content without report, the proposal is geometric: an agent tracking structured data is confined to reduced invariant manifolds whose topology reflects what it has internalized about the world, and the structure of that manifold is the candidate correlate of experiential content. Realism — whether the experience is "about" the external world — is then operationalized as MAI between manifold structure and world, separating dreaming (rich manifold, low world-coupling) from waking perception (rich manifold, high world-coupling).